Stable event structures and their duality with prime algebraic domains (arising as partial orders of configurations) are a landmark of concurrency theory, providing an elegant characterisation of causality in computations. They have been used for defining a concurrent semantics of several formalisms, from Petri nets to linear graph rewriting systems, which in turn lay at the basis of many visual frameworks. Stability however is restrictive for dealing with formalisms where a computational step can merge parts of the state, like graph rewriting systems with non-linear rules, which are needed to cover some relevant applications (such as the graphical encoding of calculi with name passing). We characterise, as a natural generalisation of prime algebraic domains, a class of domains that is well-suited to model the semantics of formalisms with fusions. We then identify a corresponding class of event structures, that we call connected event structures, via a duality result.